How do i compute $f_n = 3f_{n-1} + 2\sqrt{2f_{n-1}^2 – 2}$ for n around 10^18?

So I have the reccurence $$f_n = \begin{cases} 3f_{n-1} + 2\sqrt{2f_{n-1}^2 – 2}, &n > 0\ 3, &n > 1\ \end{cases}$$ and I need to compute it in $$\lg(n)$$, for n as big as $$10^{18}$$. I tried to reduce it to a closed form equation but I don’t see how that could be achieved.